Gibbs function continuation for the stable computation of chemical equilibrium

We consider the computation of the chemical equilibrium state of an ideal gas mixture of given elemental composition, with and without general linear constraints on the species present. While computer programs to solve these problems have been available for more than 30 years, it is found that they are not always successful in determining the chemical equilibrium state in the presence of constraints. We present here the new method of Gibbs function continuation, which is guaranteed to determine the chemical equilibrium state for all well-posed constrained and unconstrained problems.